Method of determining prior net benefit of obtaining additional risk data for insurance purposes via survey or other procedure

ABSTRACT

A method is disclosed for determining the prior net benefit of obtaining data relating to an individual risk in an insurance portfolio, via a survey or similar procedure. A risk model is developed at the individual risk level for mathematically estimating the probability of expected loss given a set of information about the risk. The risk model is incorporated into a profitability model. A probability distribution relating to the type of survey information to be obtained is developed, which is used for determining the gross value of obtaining the information. The method produces as an output a quantitative estimation (e.g., dollar value) of the net benefit of obtaining survey data for the risk, calculated as the gross value of the survey less the survey&#39;s cost, where the benefit of the survey relates to a quantitative increase in predictive accuracy resulting from incorporating the survey data into the predictive model.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation-in-part of U.S. patent application Ser. No.11/323,252, filed Dec. 30, 2005, which claims the benefit of U.S.Provisional Application Ser. No. 60/709,634, filed Aug. 19, 2005.

FIELD OF THE INVENTION

The present invention relates to data processing and, more particularly,to an automated electrical financial or business practice or managementarrangement for insurance.

BACKGROUND OF THE INVENTION

Generally speaking, commercial insurance is a form of risk allocation ormanagement involving the equitable transfer of a potential financialloss, from a number of people and/or businesses to an insurance company,in exchange for fee payments. Typically, the insurer collects enough infees (called premiums) from the insured to cover payments for lossescovered under the policies (called claims), overhead, and a profit. Eachinsured property or item, such as a plot of land, a building, company,vehicle, or piece of equipment, is typically referred to as a “risk.” Agrouping of risks, e.g., all the properties insured by an insurer orsome portion thereof, is called a “portfolio.”

At any particular point in time, each portfolio of risks has anassociated set of past claims and potential future claims. The former isa static, known value, while the latter is an unknown variable. Morespecifically, for a given portfolio in a given time period, e.g., oneyear, there may be no claims or a large number of claims, depending oncircumstances and factors largely outside the insurer's control.However, to set premiums at a reasonable level, it is necessary topredict or estimate future claims, e.g., from the insurer's perspectiveit is beneficial to set premiums high enough to cover claims andoverhead but not so high as would drive away potential customers due touncompetitive pricing. The process of mathematically processing dataassociated with a risk portfolio to predict or estimate future loss iscalled “risk modeling.” Traditionally, this has involved using actuarialmethods where statistics and probability theory are applied to a riskportfolio as a whole (i.e., with the risks grouped together), and takinginto consideration data relating to overall past performance of the riskportfolio.

While existing, actuarial-based methods for risk modeling in theinsurance industry are generally effective when large amounts of dataare available, they have proven less effective in situations with lesson-hand data. This is because the data curves generated with suchmethods, which are used to estimate future losses, are less accuratewhen less data is present—in estimating a curve to fit discreet datapoints, the greater the number of data points, the more accurate thecurve. Also, since portfolios are considered as a whole, there is no wayto effectively assess individual risks using such methods.

Risk assessment surveys are sometimes used as part of the process ofrisk modeling or management, for purposes of collecting data relating toan insurance portfolio. In a general or non-mathematical sense, riskassessment surveys may be used to identify risk management strengths andweaknesses of individual risks and/or risk portfolios. For example, if aparticular risk weakness is identified through a survey, e.g., anoutdated fire suppression system in a manufacturing plant, the insuredmay be encouraged to make appropriate changes to reduce the problem.Alternatively, premiums may be increased to compensate for the increasedrisk factor. Risk assessment surveys may also be used to harvest datafor increasing the overall data available for risk modeling.

Risk assessment surveys are typically developed and carried out by riskmanagement specialists, and may involve a series of specially selectedquestions both directly and indirectly related to the insurance coveragecarried by the insured party. The survey may also involve directinspections or observations of buildings, operations, etc. Accordingly,the costs associated with risk assessment surveys are typically notinsignificant. However, it is difficult to determine (especiallybeforehand) if the costs associated with risk assessment surveys are“worth it,” i.e., if they will provide meaningful information as tosignificantly impact risk management decisions and/or risk modelingcalculations. Heretofore, prior quantitative determinations of the valueassociated with surveys have not been possible, leaving insurers withoutan accurate tool to determine when to proceed with surveys for a risk orportfolio.

SUMMARY OF THE INVENTION

An embodiment of the present invention relates to a method fordetermining the prior net benefit of obtaining data relating to anindividual risk in an insurance portfolio, via a survey or similarprocedure, for use in a predictive model or otherwise. (By “individualrisk,” it is meant a single insured property, e.g., a building, item ofequipment, vehicle, company, person, or parcel of land, as well as agrouping of such insured properties.) The method produces as an output aquantitative estimation (e.g., dollar value) of the net benefit ofobtaining survey data for a risk, calculated as the benefit of thesurvey less the cost of the survey, where the benefit of the surveyrelates to a quantitative increase in predictive accuracy resulting fromincorporating the survey data into the predictive model. With priorknowledge of a survey's net benefit, either positive or negative, it ispossible to make a more informed decision as whether or not to carry outa survey for a particular risk.

The survey benefit method may be implemented in conjunction with arisk/loss model such as a Bayesian predictive model that combineshistorical data, current data, and expert opinion for estimatingfrequencies of future loss and loss distributions for individual risksin an insurance portfolio. The purpose of the Bayesian model is toforecast future losses for the individual risk based on the past lossesand other historical data for that risk and similar risks. In additionto the Bayesian predictive model, the method utilizes a revenue model, amodel for the cost of obtaining additional data (e.g., survey cost), andprobability distributions of population characteristics.

Initially, a risk model (e.g., a Bayesian predictive model) is developedat the individual risk level for mathematically estimating theprobability of expected loss given a set of information about the risk.The risk model is incorporated into a profitability model for the risk,which also includes premium and expense models for the risk. (Generallyspeaking, the profitability model is a statistical “expansion” of thefollowing insurance truism: profit=premiums−losses−marginal expenses.)Subsequently, a probability distribution relating to the type orcategory of information possibly to be obtained by way of a survey isdeveloped or determined, which is used as a basis for determining thegross value of obtaining the information. In particular, the gross valueis the projected profitability of the best action or outcome (e.g., ofinsuring or not insuring the risk) given the additional informationobtained from the survey, less the projected profitability of the bestaction or outcome to be expected without knowing the additionalinformation. From the gross value, the net benefit of conducting thesurvey is determined, e.g., net benefit=gross value−survey cost. If thenet benefit is positive, that is, if the benefit of conducting a surveyoutweighs the survey's cost, rational insurers will carry out thesurvey. If not, insurers may opt not to conduct the survey.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood from reading thefollowing description of non-limiting embodiments, with reference to theattached drawings, wherein below:

FIG. 1 is a schematic diagram of a system and method of predictivemodeling for estimating frequencies of future loss and lossdistributions for individual risks in an insurance portfolio;

FIGS. 2 and 5 are flow charts showing the steps of the method in FIG. 1;

FIGS. 3A-3F and 4A-4C show various equations used in carrying out themethod;

FIG. 6 is a schematic view of a system for determining the prior netbenefit of obtaining data relating to an individual risk in an insuranceportfolio, via a survey or similar procedure, according to an embodimentof the present invention; and

FIG. 7 is a flow chart showing the steps of a method carried out by thesystem in FIG. 6.

DETAILED DESCRIPTION

An embodiment of the present invention relates to a method fordetermining the prior net benefit of obtaining data relating to anindividual risk in an insurance portfolio, via a survey or similarprocedure, for use in a predictive model or otherwise. (By “individualrisk,” it is meant a single insured property, e.g., a building, item ofequipment, vehicle, company, person, or parcel of land, as well as agrouping of such insured properties.) The method produces as an output aquantitative estimation (e.g., dollar value) of the net benefit ofobtaining survey data relating to a risk, calculated as the benefit ofthe survey less the cost of the survey, where the benefit of the surveyrelates to a quantitative increase in predictive accuracy resulting fromincorporating the survey data into the predictive model. With priorknowledge of a survey's net benefit, either positive or negative, it ispossible to make a more informed decision as whether or not to carry outa survey for a particular risk.

The survey benefit method may be implemented in conjunction with a riskmodel such as a Bayesian predictive model that combines historical data,current data, and expert opinion for estimating frequencies of futureloss and loss distributions for individual risks in an insuranceportfolio. The purpose of the Bayesian model is to forecast futurelosses for the individual risk based on the past losses and otherhistorical data for that risk and similar risks. In addition to theBayesian predictive model, the method utilizes a revenue model, a modelfor the cost of obtaining additional data (e.g., survey cost), andprobability distributions of population characteristics.

Initially, a risk model (e.g., a Bayesian predictive model) is developedat the individual risk level for mathematically estimating theprobability of expected loss given a set of information about the risk.The risk model is incorporated into a profitability model for the risk,which also includes premium and expense models for the risk. (Generallyspeaking, the profitability model is a statistical “expansion” of thefollowing insurance truism: profit=premiums−losses−marginal expenses.)Subsequently, a probability distribution relating to the type orcategory of information possibly to be obtained by way of a survey isdeveloped or determined, which is used as a basis for determining thegross value of obtaining the information. In particular, the gross valueis the projected profitability of the best action or outcome (e.g., ofinsuring or not insuring the risk) given the additional informationobtained from the survey, less the projected profitability of the bestaction or outcome to be expected without knowing the additionalinformation. From the gross value, the net benefit of conducting thesurvey is determined, e.g., net benefit=gross value−survey cost. If thenet benefit is positive, that is, if the benefit of conducting a surveyoutweighs the survey's cost, rational insurers will carry out thesurvey. If not, insurers may opt not to conduct the survey.

The process for developing a Bayesian predictive model is describedbelow with reference to FIGS. 1-5. The method for determining the priornet benefit of obtaining data relating to an individual risk in aninsurance portfolio via a survey or similar procedure is describedfurther below with respect to FIGS. 6 and 7.

FIGS. 1-5 illustrate a method or system 10 of predictive modeling forgenerating a forecast of expected loss 12 for individual risks 14 a, 14b, 14 c, 14 d, etc. in an insurance portfolio 16. Typically, this willbe done for insurance-related purposes, for determining premium levelsand the like. By “individual risk,” it is meant a single insuredproperty, e.g., a building, item of equipment, vehicle,company/business, person, operation/manufacturing line, or parcel ofland. For generating the loss forecast 12, the method uses a Bayesianprocedure 18 that incorporates historical data 20 relating to theindividual risk 14 b in question. The historical data 20 will typicallycomprise information somehow relevant or related to the risk, and mayinclude any of the following: recorded losses for the risk, with date,amount and type of loss, for a given loss basis (such as paid orincurred); the period during which the risk was exposed to recordedlosses, namely, the effective and expiration dates of any policiesapplying to the risk; the terms and conditions of the policies applyingto the risk, principally deductible, limit, and coinsurance; and variouscharacteristics of the risk. For example, for a building suchcharacteristics could include value, occupancy, construction type, andaddress/location.

The Bayesian procedure 18 also utilizes historical data 20 relating tosimilar risks 22. By “similar risk,” it is meant a risk other than theindividual risk 14 b that has some logical connection or relationshipthereto, such as features or characteristics in common, at least in ageneral sense. For example, if the individual risk 14 b is a hospital,then similar risks could include other hospitals, other medicalfacilities, or even other buildings within a relevant (i.e., the same orsimilar) geographical area. The similar risks may be risks within theportfolio 16, but do not have to be. As should be appreciated, thehistorical data from the similar risks provides a significantly largerdata pool than just the historical data for the individual risk 14 b byitself. It is relevant to the loss forecast for the individual risk 14 bbecause data from a similar risk will typically tend to have somebearing on the individual risk, i.e., from a statistical orprobabilistic standpoint, similar risks will likely experience similarlosses over time. For example, if all the hospitals over a certain sizein a particular area experience at least a certain amount of loss in agiven period, such information will tend to increase the probabilitythat a similar hospital in the same area will also experience at leastthe same loss.

Expert opinion 24 relating to the individual risk 14 b is also obtainedand utilized as part of the Bayesian procedure 18 calculations. Theexpert opinion 24 acts as a baseline for calculating the loss forecast12 when little or no historical data 20 is available. Thus, wherehistorical data is unavailable, the expert opinion 24 dominates thepredictive calculation. The expert opinion 24 is typically provided as(or expressed as part of) a mathematical function or model that definesan estimated probability distribution of some aspect of the individualrisk 14 b or a related or similar risk 24. As its name implies, theexpert opinion 24 may be obtained from professionals in the field whohave studied some aspect of the individual or similar risks in question.Expert opinion may also be obtained from reference works. For aparticular portfolio, the expert opinion may collectively include inputfrom a number of professional sources, each of which relates to one ormore aspects of the individual or similar risks. In other words, whenimplementing the method 10, it may be the case that a number ofdifferent functions/models are obtained and utilized as expert opinion,to more fully characterize the individual or similar risks in theBayesian procedure 18.

As an example, in a simple case where all the risks in a portfolio aregenerally the same except for value, the frequency of loss for suchrisks might be characterized as the following probability distribution:frequency of loss=c·(v/v ₀)^(b), where

-   “c” and “b” are system parameters-   v=value-   v₀=reference size/value    Here, the equation itself might be considered expert opinion, i.e.,    obtained from a professional/expert or reference work, as might the    range of values for the system parameters “c” and “b”. For example,    given the equation and system parameters, an expert might be    consulted to provide values for “c” and “b” that give the highest    probability to fit the data. Thus, expert opinion might be solicited    for selecting the best model based on the type of data to be    modeled, as well as the best system parameters given a particular    model.

For the Bayesian procedure 18, current data 26 may also be obtained andutilized. “Current” data 26 is the same as historical data but isinstead newly obtained as the method 10 is carried out over time. Forexample, if an individual risk 14 b experiences a loss after themethod/system 10 has been implemented initially, then information aboutthis loss may be entered into the system 10 as current data 26.

FIG. 2 summarizes the steps for carrying out the method 10 forforecasting the future losses 16 for an individual risk 14 b. Asdiscussed further below, these steps may be performed in a differentorder than as shown in FIG. 2, e.g., it will typically be the case thatexpert opinion is obtained after first establishing a predictive model.At Step 100, the expert opinion 24 relating to the individual risk 14 band/or similar risks 22 is obtained. Then, at Step 102, the historicaldata 20, again relating to the individual risk and/or similar risks 22is obtained. If historical data 20 is not available, then this step willbe bypassed until historical and/or current data become available. Insuch a case, the Bayesian procedure 18 is carried out with the expertopinion 24 only, which, as noted above, acts as an estimation orbaseline.

At Step 104 in FIG. 2, the historical data 20, any current data 26, andexpert opinion 24 are combined using the Bayesian procedure 18. Theeffect of the Bayesian procedure 18 is to forecast the future losses 12for the individual risk 14 b based on the past losses and otherhistorical data 20 for that risk 14 b and similar risks 22. Typically,the Bayesian procedure 18 will utilize a Bayesian predictive model asshown by equation 28 in FIG. 3A. In equation 28, a predictiveconditional probability distribution “f (y|x)” of forecast losses (“y”)for the individual risk 14 b, given all historical data (“x”), isrepresented in terms of: (i) a probability distribution “f(y|θ)” of theforecast losses y given a system parameter set (“θ”), i.e., a forecastlosses likelihood function; (ii) a probability distribution “f(x|θ)” forthe historical data, i.e., an historical data likelihood function; and(iii) a prior probability density function of the parameter set “f(θ).”

Equation 28 in FIG. 3A is generally applicable in carrying out themethod 10. This equation is derived with reference to Steps 106-112 inFIG. 2, provided for informational purposes. To derive equation 28, atStep 106, the conditional probability distribution f(y|x) of forecastlosses y for the individual risk 14 b, given all historical data x, isrepresented as a weighted sum of , probability distributions, as shownby equation 30 in FIG. 3B. The weighted sum may be an integral of theprobability distribution f(y|θ) of the forecast losses y given thesystem parameter set θ times a parameter set weight “f(θ|x).” Here, theparameter set weight f(θ|x) is a posterior probability density functionof the system parameters θ given the historical data x. Equation 30 is astandard equation for the predictive distribution of a random variableof interest y given observed data x.

At Step 108, the probability distributions f(y|θ) for forecast losses yare arranged to depend on the parameter set θ, indexed by an index “i”.At Step 110, the probability distributions f (x|θ) for historical dataare also arranged to depend on the same parameter set θ, also indexed bythe index “i”. Next, at Step 112, the posterior probability densityfunction f (θ|x) is calculated as the probability distribution of thehistorical data given the parameter set f (x|θ), times the priorprobability of the parameter set f (θ), obtained from the expert opinion24. This is shown as equations 32 in FIG. 3C (these equations arestandard representations of Bayes' theorem for probability densities).Thus, combining equations 30 and 32, the conditional probabilitydistribution f (y|x) of forecast losses y for the individual risk 14 b,given all historical data x, is as shown by equation 28 in FIG. 3A. Thiscan be further represented by:f(y|x)=f(y|θ ₁)·p(θ₁)+f(y|θ ₂)·p(θ₂)+ . . .where each “p” is the probability of the particular respective systemparameter θ.

Starting with the predictive model 28 (FIG. 3A), the probabilitydistributions f (y|θ) and f (x|θ) are obtained for the forecast losses yand historical data x, respectively, using a compound Poisson processmodel. Generally speaking, a Poisson process is a stochastic processwhere a random number of events (e.g., losses) is assigned to eachbounded interval of time in such a way that: (i) the number of events inone interval of time and the number of events in another disjoint(non-overlapping) interval of time are independent random variables, and(ii) the number of events in each interval of time is a random variablewith a Poisson distribution. A compound Poisson process is acontinuous-time stochastic process “Y(t)” represented by equation 34 inFIG. 3D, where Y(t) represents the aggregate loss, “N(t)” is a Poissonprocess (here, the underlying rate of losses), and “X_(i)” areindependent and identically distributed random variables which are alsoindependent of “N(t)” (here, X_(i) represents the severity distributionof the losses). If full knowledge of the characteristics of a risk 14 bwere available, historical and forecast losses for that risk could beapproximated by a compound Poisson process, in which losses for eachtype of loss occur according to a Poisson process, and where the size of“ground-up” loss is sampled from a severity distribution depending onthe type of loss (ground-up loss refers to the gross amount of lossoccurring to a reinsured party, beginning with the first dollar of lossand after the application of deductions). Here, in order to accommodateheterogeneity in a class of similar risks because full knowledge of arisk's characteristics may not be available, losses for each risk aremodeled as a finite mixture of compound Poisson processes, as at Step114 in FIG. 2. As noted, the parameters of the compound Poisson processwill typically be the underlying rate of losses (N(t)) and the severitydistribution (X_(i)) of the ground-up losses, which depend on the knowncharacteristics 20 of the risk 14 b. In the case of a building, suchcharacteristics will typically include value, occupancy, constructiontype, and address, and they may also include any historicalclaims/losses for that risk.

At Step 116, the probability distribution f (y|x) is calculated orapproximated to produce the probability distribution of losses 12 forthe forecast period for the individual risk 14 b. With respect toequation 28 in FIG. 3A, the expert opinion from Step 100 is incorporatedinto the equation as the prior probability density function f (θ). Then,at Step 118, forecasts of paid claims for the individual risk 14 b maybe obtained by applying limits and deductibles to the forecast of losses12 for that risk 14 b. Generally, gross loss “Z” (see equation 36 inFIG. 3E) can be represented as the sum of losses “x_(i)” from i=1 to N,where “N” is a frequency of loss, but where each loss x is reduced byany applicable deductibles. Thus, the final outcome of the system 10 isrepresented as shown in equations 38 and 40 in FIG. 3F. At Step 120,current data 26 may be incorporated into the method/system 10 on anongoing manner.

For each individual risk 14 a-14 d, the method 10 may also be used toproduce breakdowns of forecasted expected loss by type of loss, aforecasted probability distribution of losses, a calculation of theeffect of changing limits, deductibles, and coinsurance on the lossforecast, and a forecasted expected loss ratio, given an input premium.The method 10 may also be used to produce joint probabilitydistributions of losses for a forecast period for risks consideredjointly, as indicated by 42 in FIG. 1.

The above-described Bayesian procedure for estimating the parameters ofa compound Poisson process for the purpose of predictive risk modelingwill now be described in greater detail.

For a portfolio 16, the ultimate aim of the predictive model should beto produce a probability distribution for the timing and amounts offuture claims, by type of claim, given the information available at thetime of the analysis, i.e., the historical data 20. This information 20will generally include: (i) past claims; (ii) past coverages, includingeffective dates, expiration dates, limits, deductibles, and other termsand conditions; (iii) measurements on past risk characteristics such as(in the case of property coverage) construction, occupancy, protection,and exposure characteristics, values, other survey results, andgeographic characteristics; (iv) measurements on past environmentalvariables, such as weather or economic events; (v) future coverages (ona “what-if” basis); (vi) measurements on current risk characteristics;and (vii) measurements on current and future environmental variables.Future environmental variables can be treated on a what-if basis or byplacing a probability distribution on their possible values. Forsimplicity, it may be assumed (as herein) that current and futureenvironmental variables are treated on a what-if basis.

In the formulas discussed below, the following abbreviations are used:

-   cl1=future claims occurring in the period t₀ to t₁-   cv1=actual or contemplated future coverages for the period t₀ to t₁-   rm1=measurements on risk characteristics applicable to the period t₀    to t₁-   ev1=assumed environmental conditions for the period t₀ to t₁-   cl0=future claims occurring in the period t₁ to t₀ (or more    generally, for a specified past period)-   cv0=actual past coverages for the period t₁ to t₀-   rm0=measurements on risk characteristics applicable to the period t₁    to t₀-   ev0=environmental conditions for the period t₁ to t₀

The probability distribution for the timing and amounts of futureclaims, by type of claim, given the information available at the time ofthe analysis, can be written as:p (cl1|cv1, rm1, ev1, cl0, cv0, rm0, ev0)where “p” denotes a conditional probability function or probabilitydensity where the variables following the bar are the variables uponwhich the probability is conditioned, i.e., a probability density of cl1given variables cv1, rm1, ev1, cl0, cv0, rm0, and ev0. (It should benoted that this is a more detailed rendering of the more generalizedconditional probability distribution “f (y|x)” noted above.)Construction of the predictive model begins by introducing the set ofparameters, collectively denoted by θ, which denote the riskpropensities of the risks 14 a-14 d in the portfolio 16. A standardprobability calculation results in equation 50 as shown in FIG. 4A.(Again, it may be noted that equation 50 is a more detailed equivalentof equation 28 in FIG. 3A.) Equation 50 is true regardless of theassumptions of the model.

The model assumptions now introduced are as follows. Firstly,p (cl1|cv1, rm1, ev1, cl0, rm0, ev0, θ)=p (cl1|cv1, rm1, ev1, θ)which expresses the assumption that if the loss/risk propensities θ areknown, the future claims for the portfolio depend only on the currentand future coverages, risk measurements, and environmental variables,and not on the past claims and other aspects of the past. The validityof this assumption depends on the ability to construct a model thateffectively captures the information from the past in terms of knowledgeabout risk propensities. Secondly,p (cl0|cv1, rm1, ev1, cv0, rm0, ev0, θ)=p (cl0|cv0, rm0, ev0, θ)which expresses the assumption that, provided past coverages, riskmeasurements, and environmental variables are known, knowing futurevalues for these quantities is irrelevant when considering thelikelihood of past claims data. This assumption does not exclude thecase in which present risk measurements can shed light on past riskcharacteristics, for example when a survey done more recently shedslight on risk characteristics further in the past. Thirdly,p (θ|cv1, rm1, ev1, cv0, rm0, ev0)=p (θ)which expresses the assumption that the prior probability distributionfor the risk propensities p(θ) does not depend on additionalinformation. The risk propensities can be expressed in such a way thatthis assumption is valid, for example by assigning prior probabilitydistributions of risk propensity to classes and types of risks, ratherthan to individual risks.

Given these three assumptions, the predictive model can be written asequation 52 in FIG. 4B.

The Bayesian model estimation process includes the following steps, asshown in FIG. 5. Starting with the model from equation 52 in Step 130,the future claims (losses) likelihood function p(cl1|cv1, rm1, ev1, θ)is constructed at Step 132. At Step 134, the past claims (historicaldata) likelihood function p(cl0|cv0, rm0, ev0, θ) is constructed. AtStep 136, expert opinion is obtained for the prior distribution for riskpropensities p(θ). Next, at Step 138, the Bayesian predictive model issolved or approximated. Step 140 involves model criticism and checking.

The past and future claims likelihood functions may be constructed asfollows (in the basic case). Conditional on a fixed and known value forθ, claims are considered to be generated by a multivariate compoundPoisson process, in which ground-up losses occur according to a Poissonprocess with rate λ (i, j) for risk “i” and type of loss “j” (as notedabove, the risk 14 a-14 d could be a building, an establishment, or anyother specific entity within the portfolio 16). The ground-up lossamounts are considered to be generated independently from a lossdistribution F (i, j) again depending on risk i and type of loss j. Bothλ (i, j) and F (i, j) depend on risk measurements for risk i andenvironmental variables, in such a way that

-   λ_(Past) (i, j)=g_(j) (past risk measurements for i, past    environmental variables, θ)-   λ_(Future) (i, j)=g_(j) (current risk measurements for i, current    environmental variables, θ)-   F_(Past) (i, j)=h_(j) (past risk measurements for i, past    environmental variables,θ)-   F_(Future)(i,j)=h_(j) (current risk measurements for i, current    environmental variables, θ)

The functions g_(j) and h_(j) are known functions that are designed toproduce a flexible set of representations for the way in which the lossprocess for a risk depends on the characteristics of a risk andenvironmental variables. A hypothetical example could beg _(j) (past risk measurements for i, past environmental variables,θ)=exp(a ₀+a ₁ ln(x ₁)+a ₂ x ₂+ . . .) for occupancy=A, region=X, . . .=exp(b ₀+b ₁ ln(x ₁)+b ₂ x ₂+ . . . ) for occupancy=B, region=X, . . .. . .where x,=square footage, x₂=mean winter temperature for location, . . .

In this case a₀, a₁, a₂, b₀, b₁, b₂, . . . are all elements of thecollection of parameters that is denoted by θ.

The basic model makes the assumption that the past risk propensitiesequal the future risk propensities, and the functions linking the riskpropensities to the loss process are the same in past as in the future,so that all the differences in frequency and severity between past andfuture are explained by changes in risk measurements and environmentalvariables. Extensions to the model allow for risk propensities and riskcharacteristics to evolve according to a hidden-Markov model. Anotherextension is to allow time-dependent rates for the Poisson processesgenerating the ground-up losses. This may be necessary if forecasts oftotal claims for partial-year periods are required in order to deal withseasonality issues. Allowing for seasonally changing rates also allowsfor slightly more precision in estimating the claims process. It shouldbe noted that the existing model allows for the predicted claims for arisk (i) to be influenced by the number and amount of past claims forthat same risk if coverage existed on that risk in the past.

In practice, loss distributions are parameterized by a small number ofparameters—for example, F may be lognormal with parameters μ and σ, inwhich case

-   μ_(Past)(i, j)=hμ_(j)(past risk measurements for i, past    environmental variables, θ)-   μ_(Future)(i, j)=hμ_(j)(current risk measurements for i, current    environmental variables, θ)-   σ_(Past)(i, j)=hσ_(j)(past risk measurements for i, past    environmental variables, θ)-   σFuture(i, j)=hμ_(j)(current risk measurements for i, current    environmental variables, θ)

The model uses finite mixtures of lognormal distributions in order toapproximate a wider range of loss distributions than a single lognormaldistribution can. In this case there are several values for μ and σ, onefor each component, as well as a set of mixing parameters. The extensionto the model is that now there are more functions, but each is still aknown function with unknown parameters that are part of the collectionof parameters θ.

The method described does not specify the functions linking the riskmeasurements and environmental variables to the parameters of thecompound process. Functions that have been shown to work well inpractice include linear, log-linear and power functions, and nonlinearfunctions that are piecewise continuous such as piecewise linearfunctions and natural splines. Useful are functions of linear ornonlinear combinations of several variables, such as the ratio of valueto square footage, or contents value to building value in the case ofproperty risks.

To model the claims process, given a model for the ground-up lossprocess, it is necessary to apply terms of coverage, limits anddeductibles to the modeled ground-up loss process. If no coverage is ineffect over an interval of time for a given risk, all losses generatedby the ground-up loss process during that interval of time are notobserved. Any losses below the deductible are not observed and anylosses above the limit are capped at the limit. Because of thecharacteristics of the compound Poisson process, the claims process isalso a compound Poisson process (during periods of coverage), with therate of claims for risk i and loss type j being

-   λ(i, j)*Pr(X_(i,j)>deductible_(i)) where X_(i,j) has the    distribution given by F_(i,j)-   and the size of the claims for risk i and loss type j having the    same probability distribution of that of-   min(X_(i,j)−deductible_(i), polmit_(i)) conditional on this quantity    being positive.

Once the past claims process and the future claims process have bothbeen specified in terms of two (related) compound Poisson processes, itis straightforward to write the likelihood functions for past claims andfuture claims using standard formulas. The function can be expressed insimple mathematical terms although the formula is lengthy when written.A single compound Poisson process has a likelihood function as shown byequation 54 in FIG. 4C, where “N” is the number of claims (abovedeductible), “x_(i)” are the sizes of the claims (after deductible), “λ”is the annual rate of the Poisson process, “z” is the number of yearsexposed to losses, and “f” is the probability density of the claimdistribution (there is a simple modification for distributions withmasses at a single point which occur when there is a limit).

Once θ is known, λ and f can be calculated for each combination of riskand loss type for past claims. It is assumed that losses occurindependently at each risk, conditional on θ, so the past likelihood forthe whole portfolio is just the product of factors, one factor for eachcombination of risk (i) and loss type (j), where each factor has theform given above, except that z, λ, and f depend on (i, j) and N isreplaced by N(i, j) which is the number of past claims for risk (i) andloss type (j). The same process produces the likelihood for futureclaims (z, λ, and f may be different in the future likelihood functionthan in the past likelihood function even for the same risk and losstype).

The remaining portion of the general formula involves the priorprobability distribution p(θ). This is obtained through expertelicitation, as at Step 100. Where there is sufficient loss data, theeffect of the prior probability distribution tends to be small. However,in the collection of parameters given by θ there may be some parameters(such as the frequency for a particular class of business with a smallexposure) for which there is little claim data, in which case theseparameters will be more sensitive to the expert opinion incorporated inthe prior.

Once the past and future likelihood functions and the prior distributionhave been specified, the probability distribution of predicted claimscan be obtained by solving the predictive model integral given above.This produces a probability distribution for the predicted claims foreach risk and each type of loss in the future portfolio, given coverageassumptions. Solving this sort of integral is a central topic ofBayesian computation and is the subject of extensive literature. Ingeneral, numerical techniques are required, a popular simulation methodbeing Markov Chain Monte Carlo. An alternative procedure is to obtainthe maximum likelihood estimate of θ, which is the value of θ thatmaximizes the past likelihood function. Since all the quantities besidesθ in the past likelihood function are known (these are past claims, pastcoverages, past risk measurements, and past environmental variables),this function, namelyp (cl0|cv0, rm0, ev0, θ)can be maximized as a function of θ. It is known that under mostconditions and given enough data, the likelihood, as a function of θ,can be approximated by a multidimensional quadratic surface. Experienceusing the procedure with real data reinforces this theoretical finding.If this is the case, then the probability distribution of θ, given thepast data, can be approximated as a multivariate Normal distribution. Afurther approximation uses the mean of this multivariate Normaldistribution as the single point estimate of θ (the Bayes posterior meanestimate).

Given a single point estimate of θ, the predictive distribution offuture claims is straightforward to calculate, since it is the given bythe future likelihood. The predicted future ground-up losses are givenby a compound Poisson process whose parameters are given in the simplestcase by

-   λ_(Future)(i, j)=g_(j)(current risk measurements for i, current    environmental variables, θ)-   μ_(Future)(i, j)=hμ_(j)(current risk measurements for i, current    environmental variables, θ)-   σ_(Future)(i, j)=hσ_(j)(current risk measurements for i, current    environmental variables, θ)    where θ is set to the Bayes posterior mean estimate, and the claims    compound Poisson process is obtained by applying deductible and    limit adjustments as described previously.

If the predicted annual average loss (after deductible and limit) isdesired for risk (i) and loss type (j), and if the posterior meanestimate is being used, then the average annual loss is given byλ(i,j)*Pr(X _(i,j) >d _(i))*E(min(X _(i,j) −d _(i) ,l _(i))|X _(i,j) >d_(i))where “d” and “l” refer to deductible and limit respectively. If theseverity distributions are given by mixtures of lognormals, then thisformula can be easily calculated. If a single point estimate of θ is notdesirable, then the posterior distribution of θ can be approximated by afinite distribution putting probability on a finite set of points. Inthis case the average annual loss is given by a weighted sum of termslike that above. In either case, the predictive modeling procedureproduces a calculation for that can be done quickly by a computer, anddoes not require simulation. Calculation of average annual losses bylayer is also straightforward.

The method/system 10 may be implemented using a computer or otherautomated data processing or calculation device.

FIGS. 6 and 7 show in more detail the method/system for determining theprior net benefit of obtaining survey data relating to an individualrisk or category of risks 58 in an insurance portfolio.

Initially, at Step 150 a risk model 60 is developed at the individualrisk level, if needed. If one or more models have already beendeveloped, then an existing model may be used. The risk model may be aBayesian predictive model developed according to the above. Generallyspeaking, the risk model is a mathematical model of the expected lossfor a risk having certain characteristics:

-   E (loss|basic risk info, additional risk info, offer terms, contract    accepted, loss prevention plan)-   In other words, the risk model looks at the probability or    expectation of loss given a set of information including (in this    example) basic risk information (e.g., location), additional risk    information (e.g., building characteristics), offer terms (e.g.,    policy terms, insurance limits, deductible), whether the insurance    contract has been accepted, and whether a loss prevention plan is in    place and/or the characteristics of such a loss prevention plan.

The risk model 60 is incorporated into a profitability model 62, as atStep 152. This may involve developing a premium model, as at Step 154,and an expense model, as at Step 156. Generally, the profitability modelfor a risk may be expressed as the following:E(U|offer terms_a, acceptance)=E (premium)−E (loss)−E (marginal expense)

-   Here, “U” is the profitability, “E (premium)” is the premium model    (e.g., expected premium as defined by the insurance contract), “E    (loss)” is the risk model, and “E (marginal expense)” is the expense    model, e.g., the expected value of marginal expenses of the    insurance carrier as relating to this insurance contract, as    possibly determined from expert opinion. Overall, the profitability    model sets forth the expected profit “U” given certain terms “a” and    acceptance by the insured. In other words, given that an insured    party has accepted the offer for an insurance contract having    certain terms “a,” the profitability model sets forth the expected    profit.

At Step 158, a retention model 64 is developed, that is, a model of theprobability of a potential insured party accepting a particular offer.The retention model 64 is incorporated into the calculation fordetermining the gross value associated with obtaining additionalinformation by survey. The retention model (probability of acceptance)is given as:E(U|a)=E(U|offer terms_a, acceptance)·Pr (acceptance|offerterms_a)+E(U|offer terms_a, decline)·Pr (decline|offer terms_a)

-   Here, “E (U|a)” is the expectation of profitability U given an    action “a,” e.g., offering an insurance contract. “Pr” is the    probability, e.g., the probability of a potential insured party    accepting the offer given certain offer terms “a.” As should be    appreciated, the second half of the equation (relating to a party    declining the offer) reduces to a 0 (zero) value, because there is    no expected profitability in the case where a party declines the    offer for insurance.

At Step 160, the gross value 66 of the additional information to beobtained by way of a survey is determined. Generally speaking, the grossvalue of the information is calculated as the profitability 68 of thebest action given additional information “X” less the profitability 70of the best action without knowing X. In other words, if more profit isexpected from knowing information X than from not knowing information X,then obtaining the information X has a positive gross value. This can beexpressed more precisely as follows:[Gross value]=E _(x)[max_(—) a·E(U|X, a)]−max_(—) a·E _(x)(E(U|X, a))

-   where:-   X=additional information-   E_(x)=expectation function-   max_a·E (U|X, a)=profitability of best action given additional    information X-   max_a·E_(X)(E (U|X, a))=max_a·E (U|a)=profitability of best action    w/o X-   max_a=payoff for best possible action-   As part of this determination, it will typically also be necessary    to obtain the probability distribution 72 of the additional    information X, that is, the marginal distribution of the additional    information. The probability distribution may be obtained from    expert opinion and/or historical data.

As a simple example of the above, suppose that an insurance carrierinsures warehouses 58 within a certain geographical area, e.g., themanufacturing district of a city. Additionally, suppose that all thewarehouses either have a flat roof or a sloped or pitched roof. Furthersuppose that past insurance contracts have resulted in an average of $40profit (per time period) for warehouses with pitched roofs, and anaverage loss of −$100 for warehouses with flat roofs. The relevant issueis whether it is “worth it” to determine beforehand, via a surveyprocedure 73, if a prospective warehouse has a sloped roof or a flatroof 74, prior to the insurance carrier agreeing to insure thewarehouse.

From expert opinion and/or historical data, the probability of theadditional information is determined or estimated in advance. Here, forexample, suppose 20% of all warehouses have flat roofs, and 80% havepitched roofs. Without a survey 73, and thereby without knowing whethera particular warehouse has a flat or pitched roof 74, the insurancecarrier will insure all proffered warehouses, e.g., the insurer has noreason for declining any particular warehouse. (Additionally supposethat the warehouses accept the offered insurance under a standardcontract.) In this case, the expected profitability of the best action(e.g., insuring all warehouses) without knowing the additionalinformation is given as the following:(20%)(−$100)+(80%)(+$40)=+$12In other words, out of 100 warehouses seeking insurance, 100 are offeredand accept insurance. Out of these, 20 will have flat roofs with a totalexpected loss of −$2000, and 80 will have pitched roofs with a totalexpected profit of +$3200. This results in a net profit of +$1200, or$12/warehouse.

If a survey 73 is conducted, the insurer will know in advance that aparticular warehouse has a flat or pitched roof 74. In such a case,knowing that a flat roof results in an average loss, a rational insurerwill decline all flat-roofed warehouses. Thus, the profitability of thebest action (e.g., insuring only pitched-roof warehouses) given theadditional information as to roof type is as follows:(20%)($0→insurance is declined, therefore no profit orloss)+(80%)(+$40)=$32In other words, out of 100 warehouses seeking insurance, the 20 havingflat roofs are denied insurance, while the 80 having sloped roofs aregranted insurance, resulting in $3200 profit, or $32/warehouse among all100 warehouses.

The gross value of the additional data=$32−$12=$20/warehouse. In otherwords, the profit for insuring 100 randomly selected warehouses would be$1200, while the profit for only insuring the 80 of those warehouseshaving pitched roofs (as determined from a survey) would be $3200. Thegross benefit of conducting the survey is $2000, or $20/warehouse.

From the gross value of the additional information, the net value 76 isobtained, as at Step 162. The net value 76 is calculated as the grossvalue 66 less the expenses 78 associated with obtaining the additionalinformation, e.g., the cost of the survey:net value=gross value−cost/surveyThe cost per survey can be a standard value, or a value otherwiseobtained by consulting with experts or survey firms or professionals.For example, there might be a general cost associated withdeveloping/writing the survey, and a cost associated with carrying outthe survey for each property/risk, e.g., labor costs for a worker tocarry out the survey at each property/risk.

The net value will inform the decision of whether to carry out a survey73. If the net value is negative, then it is more likely that a surveywill not be carried out. If the net value is positive, that is, if thegross value exceeds the associated survey costs, then it is more likelythat a survey will be carried out to obtain survey data 74 beforecontracting to insure a particular risk.

The types of information to consider for possibly obtaining by surveywill depend on the nature of the risk. Examples include creditcharacteristics, prior loss history, location characteristics,construction characteristics, and the age and condition of buildingfixtures. Additionally, it will typically be the case that the surveyinformation is correlated to some other characteristic or set ofcharacteristics of the property, e.g., location, occupancy, age, andsize, which act as the basic drivers for especially the risk model.

The following sections provide another simplified example illustratingthe elements of a value of information calculation for a hypotheticalinsurance survey. In this example, there is a class of prospectiveinsurance risks (such as commercial establishments) with some knowncharacteristics, as determined by information on an insuranceapplication, for example. However, additional information may beobtained about these risks using certain measurements that incur costs,for example, the information may be obtained via a phone survey or via amore costly on-site survey. Suppose that the phone survey can accuratelyclassify the age of a building or equipment system into classes: (A)0-10 years, (B) 10-25 years, and (C) 25 years or older. Further supposethat the on-site survey can in addition accurately classify thecondition of the system into the classes: (a) good for its age class,(b) average for its age class, and (c) poor for its age class. Thefollowing calculations give the value of information for a per phonesurvey and per site survey. The value of information is in dollars, forthis example, and the net benefit of the information would be obtainedby subtracting the cost of obtaining the information from the value ofthe information. The possible actions of the insurer could include: (1)perform no survey, or (2) perform a phone survey, or (3) perform a sitesurvey, followed in all cases by either offering a policy having a lowerpremium (rate 1), offering a policy having a higher premium (rate 2), ordeclining to offer coverage. Additional strategies might be available tothe insurer, such as performing a phone survey and then performing asite survey in some cases, depending on the results of the phone survey.These will not be considered in this example, although thevalue-of-information calculations are similar.

The following elements are used for the calculation, which may have beenobtained through a combination of historical or sample data analysis,model-fitting, expert opinion, or the like.

Table 1 below shows the population breakdown by age and condition,knowing only that the prospect belongs to the given class of risks:

TABLE 1 Condition a b c Total Age A 6% 21% 3% 30% B 8% 28% 4% 40% C 6%21% 3% 30% Total 20% 70% 10% 100%

Tables 2a and 2b below show the expected marginal net revenue perpolicy, conditional on the policy being written at either rate 1 or rate2:

TABLE 2a Offered and accepted rate 1 Condition Age a b c A 4000 30001000 B 3000 1000 −5000 C 1000 −1000 −10000

TABLE 2b Offered and accepted rate 2 Condition Age a b c A 6000 50003000 B 5000 3000 −3000 C 3000 1000 −8000These values would typically be obtained from a risk model combined withpremium and cost data. Assume that the marginal net revenue is zero ifthe policy is not written.

Tables 3a and 3b show the rate of acceptance by the prospect of theinsurer's offer, conditional on the policy being offered at either rate1 or rate 2:

TABLE 3a Probability of Insured Acceptance, conditional on insureroffer, Rate 1 Condition Age a b c A 0.6 0.6 0.7 B 0.6 0.7 0.7 C 0.7 0.70.8

TABLE 3b Probability of Insured Acceptance, conditional on insureroffer, Rate 2 Condition Age a b c A 0.2 0.2 0.5 B 0.2 0.5 0.6 C 0.4 0.60.6In the context of policy renewals, this would be termed a retentionmodel. In either new business or renewal contexts, this model might beobtained through a combination of price elasticity studies or expertopinion.

Given these three elements, the following can be calculated.

Tables 4a and 4b below show the expected marginal net revenue perpolicy, conditional on the policy being offered at either rate 1 or rate2. In the simplest case, this is obtained by multiplying Tables 2a/2band Tables 3a/3b. The calculation may be more complex if adverseselection or moral hazard is modeled, as in the case of an insuranceprospect that accepts a high premium offer because it is aware ofhazards unknown to the insurer.

TABLE 4a Rate 1 Condition Age a b c A 2400 1800 700 B 1800 700 −3500 C700 −700 −8000

TABLE 4b Rate 2 Condition Age a b c A 1200 1000 1500 B 1000 1500 −1800 C1200 600 −4800

From this, one can obtain the optimal insurer action for eachcombination of age and condition, as shown in Table 5a:

TABLE 5a Optimal insurer offer Condition Age a b c A rate 1 rate 1 rate2 B rate 1 rate 2 decline C rate 2 rate 2 declineThe expected marginal net revenue can be obtained for each combinationof age and condition, as shown in Table 5b:

TABLE 5b Expected net revenue given insurer optimal strategy ConditionAge a b c A 2400 1800 1500 B 1800 1500 0 C 1200 600 0For example, the optimal insurer offer for (A)(a) is to offer rate 1,whose expected payoff is $2400. The weighted average of the optimalstrategy payoffs, weighted by the prevalence of each class, gives theoverall expected net revenue for a portfolio of risks, randomlydistributed according to Table 1. This quantity is $1329 and is theexpected payoff per prospect under the site survey strategy.

In comparison, for the no-survey strategy, the same action must beapplied to all the cells in the above tables, since there is noinformation available to classify the risks as above. In this case, theoptimal strategy becomes:

TABLE 6a Optimal insurer offer Condition Age a b c A rate 2 rate 2 rate2 B rate 2 rate 2 rate 2 C rate 2 rate 2 rate 2

TABLE 6b Expected net revenue given insurer optimal strategy ConditionAge a b c A 1200 1000 1500 B 1000 1500 −1800 C 1200 600 −4800The expected payoff under this strategy is the weighted average of Table6a, weighted by Table 1. This quantity is $809, and is the expectedpayoff per prospect under the no-survey strategy. To check that this isthe optimum, replace the rate 2 tables with the rate 1 tables andperform the same calculation.

The difference between the two expected payoffs is the value ofinformation, which in this case is $520 per prospect. If the marginalcost of a site survey were less than $520, the expected net benefitcriterion would suggest adopting the site survey strategy and performinga site survey for all prospects in this class, given a choice betweenthe two strategies.

The optimum set of actions under the phone survey strategy can be shownto be:

TABLE 7a Optimal insurer offer Condition Age a b c A rate 1 rate 1 rate1 B rate 2 rate 2 rate 2 C rate 2 rate 2 rate 2

TABLE 7b Expected net revenue given insurer optimal strategy ConditionAge a b c A 2400 1800 700 B 1000 1500 −1800 C 1200 600 −4800This yields an expected payoff of $1025, and a value of information of$216 per prospect. If, for example, the marginal cost of a site surveywere $600 and that of a phone survey were $100, the best of the three(simple) strategies according to the net benefit criterion would be thephone survey.

Since certain changes may be made in the above-described method fordetermining the prior net benefit of obtaining data relating to anindividual risk in an insurance portfolio via a survey or similarprocedure, without departing from the spirit and scope of the inventionherein involved, it is intended that all of the subject matter of theabove description or shown in the accompanying drawings shall beinterpreted merely as examples illustrating the inventive concept hereinand shall not be construed as limiting the invention.

What is claimed is:
 1. A system for determining a priori benefit ofconducting an insurance survey, said system comprising an automated dataprocessor configured to perform the steps of: obtaining at least oneprobability distribution of information expected to be obtained by asurvey, said information relating to at least one insurance risk; anddetermining an expected gross value of obtaining the information basedat least in part on said at least one probability distribution and aprofitability model associated with said information.
 2. The system ofclaim 1, wherein said automated data processor is further configuredfor: determining a projected cost associated with conducting the survey;and determining a net value of obtaining the information as the expectedgross value less the projected cost.
 3. The system of claim 2, whereinsaid automated data processor is further configured for: determiningwhether to conduct the survey based at least in part on the net value.4. The system of claim 3 wherein the gross value is further based atleast in part on a retention model for said at least one insurance risk,said retention model incorporating information relating to terms of aninsurance contract for said at least one insurance risk.
 5. The systemof claim 3, wherein said automated data processor is further configuredfor: conducting the survey if the net value is a positive monetaryvalue.
 6. The system of claim 1 wherein the profitability modelincorporates a risk model associated with said at least one insurancerisk, said risk model setting forth an expected insurance loss of saidat least one insurance risk given one or more characteristics of said atleast one insurance risk.
 7. The system of claim 6 wherein the riskmodel is a Bayesian predictive model.
 8. An insurance survey developmentsystem comprising an automated data processor configured to perform thesteps of: calculating the net value of obtaining information through asurvey prior to carrying out the survey, said information relating to atleast one insurance risk; and determining whether to conduct the surveybased at least in part on the net value.
 9. The system of claim 8,wherein calculating the net value of obtaining information includes thesteps of: obtaining at least one probability distribution of theinformation to be obtained by the survey; and calculating an expectedgross value of the information based at least in part on said at leastone probability distribution and a profitability model associated withsaid information, wherein the net value is based at least in part on theexpected gross value.
 10. The system of claim 9, wherein calculating thenet value of obtaining information includes the step of: determining aprojected cost associated with conducting the survey, wherein the netvalue is calculated as the gross value less the cost.
 11. The system ofclaim 10 wherein the gross value is further based at least in part on aretention model for said at least one insurance risk, said retentionmodel incorporating information relating to terms of an insurancecontact for said at least one insurance risk.
 12. The system of claim 9wherein the profitability model incorporates a risk model associatedwith said at least one insurance risk, said risk model setting forth anexpected insurance loss of said at least one insurance risk given one ormore characteristics of said at least one insurance risk.
 13. The systemof claim 12 wherein the risk model is a Bayesian predictive model. 14.The system of claim 8, wherein said automated data processor is furtherconfigured to perform the step of: conducting the survey if the netvalue is a positive monetary value.
 15. An insurance survey developmentsystem comprising an automated data processor configured to perform thesteps of: calculating a monetary value associated with information to beobtained by way of a survey procedure, prior to conducting the surveyprocedure, wherein the information relates to at least one insurancerisk; and determining whether to conduct the survey based at least inpart on the calculated monetary value.
 16. The system of claim 15,wherein said automated data processor is further configured to performthe steps of: obtaining at least one probability distribution of saidinformation; and calculating a gross value of the information based atleast in part on said at least one probability distribution and aprofitability model associated with said information, wherein themonetary value is a net value calculated based at least in part on thegross value.
 17. The system of claim 16, wherein said automated dataprocessor is further configured to perform the steps of: determining acost associated with the survey procedure, wherein the net value iscalculated as the gross value less the cost.
 18. The system of claim 17wherein the gross value is further based at least in part on a retentionmodel for said at least one insurance risk, said retention modelincorporating information relating to terms of an insurance contact forsaid at least one insurance risk.
 19. The system of claim 16 wherein theprofitability model incorporates a risk model associated with said atleast one insurance risk, said risk model setting forth an expectedinsurance loss of said at least one insurance risk given one or morecharacteristics of said at least one insurance risk.
 20. The system ofclaim 19 wherein the risk model is a Bayesian predictive model.